Applications for number of paths?

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Discussion Overview

The discussion revolves around the application of a method for determining the number of possible paths between points in space, specifically using adjacency matrices. Participants explore whether this method has real-world applications, particularly in logistics and transportation.

Discussion Character

  • Exploratory, Debate/contested

Main Points Raised

  • One participant introduces a method for calculating the number of paths between points in space, questioning its real-world applications.
  • Another participant suggests that UPS may find this method useful.
  • Several participants argue that UPS has specific criteria for path selection, such as shortest time, distance, or expense, which this method does not address since it only provides the number of paths without ranking them.
  • A later reply acknowledges the limitation of the method, emphasizing that knowing the number of paths does not help in choosing the most efficient one.
  • One participant expresses skepticism about the utility of the method but notes that unexpected applications can sometimes arise.

Areas of Agreement / Disagreement

Participants generally agree that the method's limitation in not providing specific paths or rankings makes it less useful for practical applications like those of UPS. However, there is some acknowledgment that unexpected usefulness may still exist.

Contextual Notes

The discussion highlights the dependence on the criteria for path selection and the limitations of the method in providing actionable insights.

nomadreid
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Given a set of points in space, there is a nice little method (using adjacency matrices, but this detail is not essential to the question) to determine how many possible paths there are from one point to another. Fine, but are there any real-world applications for this?
 
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UPS thinks so. :smile:
 
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Thanks, phinds, but UPS has criteria as to which path to take: the shortest in time or distance or expense, usually. This method doesn't allow any ranking in the paths; it only gives the number of paths. I don't see that UPS would find that very interesting.
 
nomadreid said:
Thanks, phinds, but UPS has criteria as to which path to take: the shortest in time or distance or expense, usually. This method doesn't allow any ranking in the paths; it only gives the number of paths. I don't see that UPS would find that very interesting.
My point is that if you don't know what all the paths are, how can you possibly choose the most efficient one, no matter WHAT criteria you use?
 
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Valid point, except that this method does not tell you what the paths are, just how many of them there are.
 
nomadreid said:
Valid point, except that this method does not tell you what the paths are, just how many of them there are.
Ah. I didn't realize that. Yeah, I don't think that sounds helpful to anyone but it's amazing how sometimes things turn out to be useful in unexpected ways.
 
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